Early illicit drug use and the age of onset of homelessness

Transcription

1 J. R. Statist. Soc. A (2019) 182, Part 1, pp Early illicit drug use and the age of onset of homelessness Duncan McVicar, Queen s University Belfast, UK, and Institute of Labor Economics, Bonn, Germany Julie Moschion University of Melbourne, Australia, and Institute of Labor Economics, Bonn, Germany and Jan C. van Ours Erasmus University Rotterdam, The Netherlands, University of Melbourne, Australia, Tinbergen Institute, Amsterdam, The Netherlands, Centre for Economic Policy Research, London, UK, and Institute of Labor Economics, Bonn, Germany [Received November Final revision July 2018] Summary.We investigate the effect of taking up daily use of cannabis on the onset of homelessness by using Australian data.we use a bivariate simultaneous mixed proportional hazard model to address potential biases due to common unobservable factors and reverse causality. We find that taking up daily use of cannabis substantially increases the probability of transitioning into homelessness for young men but not young women. In contrast, the onset of homelessness increases the probability of taking up daily use of cannabis for young women but not for young men. In a trivariate extension we find that the use of other illicit drugs at least weekly has no additional effect on transitions into homelessness for either gender but there is a large if imprecisely estimated effect of onset of homelessness on taking up weekly use of such drugs for young women. Keywords: Bivariate duration model; Cannabis; Drug use; Homelessness; Simultaneous duration model; Timing of events; Trivariate duration model 1. Introduction There is a growing quantitative social science literature on the effects of using illicit drugs such as cannabis or cocaine at a young age on a variety of health and social outcomes. One strand of this literature examines drug use effects on educational attainment, with many studies suggesting negative effects (e.g. Bray et al. (2000), Register et al. (2001), Roebuck et al. (2004), Chatterji (2006), Duarte et al. (2006) and Van Ours and Williams (2009)) and some suggesting no effect (e.g. McCaffrey et al. (2010) and Cobb-Clark et al. (2015)). Another strand of the literature concerns drug use effects on wages and other labour market outcomes, where estimated effects range from positive (e.g. Kaestner (1991) on wages), through zero (e.g. Kaestner (1994) and Zarkin et al. (1998) on hours worked, and McDonald and Pudney (2000) on occupational Address for correspondence: Duncan McVicar, Queen s Management School, Queen s University Belfast, Riddel Hall, 185 Stranmillis Road, Belfast, BT9 5EE, UK. d.mcvicar@qub.ac.uk 2018 Royal Statistical Society /19/182345

2 346 D. McVicar, J. Moschion and J. C. van Ours status), to negative (e.g. DeSimone (2002) on employment, and McDonald and Pudney (2000) on (avoiding) unemployment). Adverse effects have also been found on mental and physical health (e.g. Van Ours and Williams (2011, 2012) and Van Ours et al. (2013)). All these studies attempt to deal with the likely endogeneity of drug use, albeit with mixed success, using a variety of approaches (most commonly instrumental variables). In general, this literature suggests the younger the age of onset of drug use the bigger the detrimental effect. For recent reviews see Hall (2015) and Van Ours and Williams (2015). In this paper we examine another key social outcome the onset of homelessness that has been widely mooted, but not yet convincingly established, as a possible consequence of early illicit drug use. Several studies have demonstrated a strong positive association between youth homelessness and substance abuse (e.g. Greene et al. (1997), Mallett et al. (2005) and Shelton et al. (2009)). Others have gone further by specifically examining associations between early substance use and the onset of homelessness including in the context of multivariate regression models, with mixed results (e.g. Johnson and Fendrich (2007), Johnson and Chamberlain (2008) and van den Bree et al. (2009)). No existing study, however, has satisfactorily addressed the likely endogeneity of drug use in this case, whether stemming from selection on unobservables (i.e. that early illicit drug users are likely to be different from non-users in ways that are associated with the onset of homelessness but that we do not observe) or simultaneity (homelessness may impact on drug use as well as vice versa). This is also the case in the wider homelessness substance abuse literature with the partial exception of McVicar et al. (2015) which used longitudinal data from the Australian Journeys home (JH) study to estimate the effect of changes in substance use on changes in homelessness status by using individual fixed effects models. Conditionally on these fixed effects they found no effect of cannabis use or other illicit drug use on homelessness, although they did find an effect of heavy alcohol use. In other words, once you have been homeless and almost all of the sample that was studied by McVicar et al. (2015) had prior experience of homelesssness changes in drug use behaviour have little effect on changes in homelessness status. Neither McVicar et al. (2015) nor any other existing study, however, presents convincing quantitative evidence on whether the initial take-up of drug use behaviours impacts on the probability of becoming homeless for the first time, i.e. onset of homelessness. To address this important gap in the homelessness and substance use literatures we use information from the JH study on the ages at which individuals first engage in regular use of illicit drugs and first become homeless to estimate bivariate and trivariate simultaneous duration models allowing for common unobserved factors to influence the onset of both homelessness and substance use behaviours. Specifically, we examine whether daily use of cannabis impacts on the hazard rate for becoming homeless for the first time, and vice versa, conditionally on these unobserved factors and other observables. In an extension we examine whether the use of other illicit drugs at least weekly additionally impacts on the hazard rate for becoming homeless and vice versa. In the absence of valid instruments or natural experiments for substance use and homelessness, exploiting information about the timing of transitions into drug use and homelessness allows us to make causal inferences about how one impacts the other under plausible assumptions. The programs that we were used to analyse the data can be obtained from 2. Data Journeys home Whereas earlier studies of homelessness are based on specific groups of homeless we focus on a broader population. Rather than providing information about inviduals who sleep rough

3 Drug Use and Onset of Homelessness 347 or stay in emergency accommodation a group which Curtis et al. (2013) referred to as the acute homeless in particular geographic areas, JH is a longitudinal data set on disadvantaged Australians who are not necessarily homeless but are facing or have faced some form of housing instability during their life. Specifically, the JH sample comprises recipients of any income support (i.e. welfare) payment in Australia who are either homeless or at risk of homelessness (Wooden et al., 2012). (The at-risk category includes people flagged by Centrelink the agency that administers welfare benefits in Australia as at risk of homelessness and people identified by the research team as vulnerable to homelessness, i.e. people who have not been flagged but nevertheless have characteristics that are similar to those that have been (using a propensity score matching approach). Local Centrelink office staff are required to flag customers whom they determine to be either homeless or at risk of homelessness. Individuals flagged as homeless are without conventional accommodation (e.g. sleeping rough, squatting or living in a car), or living in or moving frequently between temporary accommodation arrangements (e.g. with friends or extended family, emergency accommodation or youth refuges). A person who is flagged at risk of homelessness lives medium to long term in a boarding house, caravan park or hotel, where accommodation is not covered by a lease, lives in accommodation which falls below the general community standards which surround health and wellbeing, such as access to personal amenities, security against threat, privacy and autonomy, is facing eviction, lives in accommodation that is not of an appropriate standard which may be detrimental to their physical and mental wellbeing, or where they have no sense of belonging or connection (e.g. indigenous Australians living in crowded conditions or disconnected from their land, family or kin, spiritual and cultural beliefs and practices). For further details see Wooden et al. (2012).) We use the first three waves collected between September 2011 and November 2012 focusing on the balanced panel, i.e. the 1347 respondents who were interviewed in all three waves of the survey and for whom, crucially, we have retrospective information on the onset of homelessness (collected in wave 1) and the onset of illicit drug use (collected in wave 3). (The JH sample contains 1682 respondents in wave 1. Differences between the characteristics of the three-wave balanced panel and wave 1 respondents are minor (see Melbourne Institute (2013)), and we find no statistically significant differences in sample means of observable controls between the two samples.) The fact that the JH survey targets a disadvantaged population makes it particularly well suited to analyse behaviours such as intense drug use and events such as the onset of homelessness which are seldom observed in the general population. The trade-off, of course, is that relationships that are observed in the JH sample may not generalize to the wider population. Homelessness can be defined in different ways and with different thresholds. JH adopts a broad conceptualization of homelessness which is very similar to that under the US 2009 Homeless Emergency Assistance and Rapid Transition to Housing Act, and similar to that used by Link et al. (1994) and Curtis et al. (2013) in the USA or Johnson and Chamberlain (2008) in Australia. Under this definition, homelessness is defined as sleeping rough or squatting in abandoned buildings, staying with relatives or friends temporarily with no alternative (doubling up), or staying in a caravan, boarding house, hotel or crisis accommodation. We construct for each respondent the age at which (s)he became homeless for the first time using this definition but also exploring sensitivity to how homelessness is defined. If the respondent has been homeless before JH wave 1 we use the retrospective information that was collected at wave 1 on How old [she was] the first time that [she was] without a place to live. (The relevant question asks :::have you ever stayed in any of the following places because you did not have a place to live? with the following options: stayed with relatives temporarily (because you did not have a place to live); stayed at a friend s house temporarily (because you did not have a place to live); stayed in a caravan, mobile home, cabin, houseboat (because you did not have a place

4 348 D. McVicar, J. Moschion and J. C. van Ours Table 1. Definition of explanatory variables Variable Definition Parents separated Parents dead Conflict with parents Emotional abuse Physical violence Sexual violence Male caregiver substance abuse Male caregiver jail Male caregiver hospital Male caregiver unemployed Male caregiver gambling Female caregiver substance abuse Female caregiver jail Female caregiver hospital Female caregiver unemployed Female caregiver gambling Missing info reason Missing info violence Missing info father Missing info mother Respondent not living with parents at age 14 years because they were divorced or separated Respondent not living with parents at age 14 years because they were dead Respondent not living with parents at age 14 years because of conflict with parents Emotional abuse or neglect as a child Physical violence as a child Sexual violence as a child Male caregiver had an alcohol or drug problem Male caregiver spent time in jail Male caregiver spent time in hospital overnight because had mental health problems Male caregiver was unemployed more than 6 months Male caregiver had a gambling problem Female caregiver had an alcohol or drug problem Female caregiver spent time in jail Female caregiver spent time in hospital overnight because had mental health problems Female caregiver was unemployed more than 6 months Female caregiver had a gambling problem Missing information on reason not living with parents at age 14 years Missing information on violence and abuse during childhood Missing information on the male caregiver s variables Missing information on the female caregiver s variables to live); stayed at a boarding house or hostel (because you did not have a place to live); stayed in a hotel or motel (because you did not have a place to live); stayed in crisis accommodation or a refuge; squatted in an abandoned building; slept rough (such as sleeping in cars, tents, trains or anywhere else outdoors) (because you did not have a place to live); other (because you did not have a place to live) (specify).) If the respondent was not homeless before JH we use the information that was collected at every wave on the type of accommodation that the respondent lived in between waves to construct her homelessness status between those waves and from this we derive the age of first onset. Although we cannot rule out recall error in the reported age at which the individual first experienced homelessness, systematic under-reporting of prior homelessness seems unlikely here given the nature of the survey. Only 7% of wave 1 respondents report never having been homeless. Similarly, we use retrospective information that was collected in wave 3 about the age at which respondents first used cannabis daily or, in the extension, first used illegal or street drugs other than cannabis (at least weekly). Again we cannot rule out recall error in the reported age at which the individual first engaged in these behaviours. Nor can we entirely rule out systematic under-reporting of drug use of the kind that was discussed by Brown et al. (2018), although only 20% (52%) of the wave 1 sample reported never having used cannabis (illegal drugs other than cannabis). JH also collects information on a large number of potential childhood risk factors for illicit drug use and for homelessness. We use these as controls in our empirical model for the onset of homelessness (Table 1). Sample means for these variables are reported in Table 2, separately by gender, and give a good indication of the disadvantaged nature of the JH sample. For example note the high proportions of respondents who reported having experienced physical violence,

5 Drug Use and Onset of Homelessness 349 Table 2. Sample means of control variables, balanced panel, by gender Variable Results Results for women for men Parents separated Parents dead Conflict with parents Emotional abuse Physical violence Sexual violence Male caregiver substance abuse Male caregiver jail Male caregiver hospital Male caregiver unemployed Male caregiver gambling Female caregiver substance abuse Female caregiver jail Female caregiver hospital Female caregiver unemployed Female caregiver gambling Missing info reason Missing info violence Missing info male caregiver Missing info female caregiver Total emotional abuse or sexual violence as a child (the last particularly but not only for women). Also note high rates of substance abuse, long-term unemployment, hospitalization for mental health problems and incarceration among caregivers. Finally, Although we use all sample members in our analysis, because we are primarily interested in relationships between early illicit drug use and youth homelessness we censor onsets which occur at ages older than 30 years, although we later explore sensitivity to this restriction. 3. Onset of homelessness and illicit drug use Fig. 1 presents hazard rates for first using cannabis daily and first episode of homelessness, i.e. the probability of starting to use regularly or to become homeless conditionally on not having done so already. Hazard rates for using cannabis daily are especially high at younger ages, with spikes more pronounced for males than females. For instance, at age 16 years, 13% of males who have not already started to use cannabis daily reported starting daily use of cannabis. The take-up of heavy cannabis use also peaks at 16 years old for females, with 8% reporting the onset of daily use. The onset of homelessness also peaks between the ages of 15 and 18 years (women) and 16 and 19 years (men), at above 10% in each year. Fig. 2 shows the corresponding cumulative probability distributions for the uptake of daily use of cannabis and the onset of homelessness, separately for males and females. It shows that the uptake of daily use of cannabis increases sharply between age 13 and age 18 years for both men and women. It then levels off with few respondents starting after the age of 20 years. (Uptake of any cannabis use (i.e. not restricted to daily use) shows an even steeper rise to around 70% for men and 60% for women by age 18 years followed by a similar levelling off. Van Ours and

6 350 D. McVicar, J. Moschion and J. C. van Ours Transition rate.1.08 Transition rate Age (a) Age (b) Transition rate.1.08 Transition rate Age (c) Age Fig. 1. Transition rates into (a), (b) homelessness and (c), (d) daily cannabis use by age 30 years: (a), (c) men; (b), (d) women Williams (2015) presented comparable figures drawn from survey data representative of all year olds in Australia, showing slower and later take-up reaching around 50% rather than 75% by age 30 years and with a less pronounced spike which occurs 2 years later than for the JH sample. McVicar et al. (2015) showed that the prevalence of other forms of substance use is also much higher among the JH sample than among the wider Australian population.) (d)

7 Drug Use and Onset of Homelessness 351 Fig. 2. Cumulative starting probabilities for the uptake of daily use of cannabis ( ) and the onset of homelessness ( ) by age 30 years: (a) men; (b) women

8 352 D. McVicar, J. Moschion and J. C. van Ours Table 3. Prevalence and onset of homelessness and daily use of cannabis by age 30 years Men Ever (%) Women Mean age of onset (years) Men Women Homelessness Cannabis daily N Table 4. Association between the timing of homelessness and substance use by age 30 years Results for men Results for women (%) (%) Drugs before Same age Homelessness before Not homeless, drugs No drugs, homeless Not homeless, no drugs N Note that males are much more likely than females to use cannabis daily. This gender imbalance in intensity of cannabis use is also found elsewhere (e.g. Van Ours et al. (2013)). The onset of homelessness also increases sharply until around 18 years old for both genders. It then continues to increase at a slower pace up to age 30 years. In contrast with the take-up of regular use of cannabis both the proportions and the timing of the onset of homelessness are very similar for males and females. Table 3 gives summary statistics for the prevalence rates and the age of onset of daily use of cannabis and homelessness up to age 30 years for our sample. Almost all the JH sample experienced homelessness at some stage in their life 97% of women and 98% of men and 78% of women and 77% of men did so by age 30 years. On average, respondents who became homeless by 30 years old did so at an average of about 18 years old. Daily use of cannabis is also highly prevalent in our sample with 33% of females and 56% of males reporting having done so by the age of 30 years. If the association between daily use of cannabis and homelessness represents a causal relationship from drug use to homelessness, then the take-up of drug use should, on average, precede the onset of homelessness. If anything, for women, Figs 1 and 2 seem to suggest the opposite; the proportion experiencing onset of homelessness appears to lead the proportions taking up regular use of cannabis, and transitions into homelessness begin to peak before the peak in drug use. For men, Figs 1 and 2 are ambiguous in this respect. At the same time the average age of onset for cannabis use precedes that of homelessness (Table 3).

9 Drug Use and Onset of Homelessness 353 Table 5. Stated factors contributing to first homelessness Results for Results for Results for balanced homelessness homelessness panel (%) before or at after 30 years (%) 30 years (%) Women Financial difficulties Relationship breakdown or conflict Domestic and family violence or abuse Non-family violence Employment problems or unemployment Mental health issues Other health or medical issues Problematic drug or substance use Problematic gambling Transition from state care Was evicted or asked to leave by landlord Natural disaster or fire End of lease Other N Men Financial difficulties Relationship breakdown or conflict Domestic and family violence or abuse Non-family violence Employment problems or unemployment Mental health issues Other health or medical issues Problematic drug or substance use Problematic gambling Transition from state care Was evicted or asked to leave by landlord Natural disaster or fire End of lease Other N The table includes 584 women and 654 men (i.e. fewer than the 639 women and 708 men in our sample) because 55 women and 54 men did not respond to this specific question. Table 4 takes a closer look at this question by tabulating the probability that is associated with the possible combinations of timing of events with respect to the onset of homelessness and daily cannabis use uptake in the raw data, separately by gender. It shows that 12% of females and 13% of males became homeless before using cannabis daily, that 6% of females and 6% of males became homeless in the same year as they started using cannabis daily, and that 11% of females and 28% of males first became homeless after they started to use cannabis daily. In other words, daily use of cannabis can occur before, coincident with or after the onset of homelessness, with no discernible tendency for one to precede the other among young women, although there is a tendency for daily use of cannabis to precede the onset of homelessness among young men. If drug use leads to homelessness for at least some of our sample then we might expect some respondents to report drug use as a factor in their becoming homeless when asked the following

10 354 D. McVicar, J. Moschion and J. C. van Ours (wave 1) question: What led to you being without a place to live the first time?, for which problematic drug or substance use is one of 13 specified options. (Multiple responses were permitted for this question.) For the wave 1 cross-section sample, Scutella et al. (2012) found that problem drug use was the fourth most common response, with 10% of those who had been homeless at some stage reporting this as a factor in their onset of homelessness. (The most common response was relationship/family breakdown or conflict (62%), followed by domestic and family violence or abuse (19%) and financial difficulties (16%).) Restricting to the threewave balanced panel and splitting the sample into those who first experienced homelessness prior or post age 30 years (Table 5) shows that problem drug use is more frequently cited among the former group than the latter, particularly among women. Other commonly stated factors that differ markedly by age include relationship breakdown and domestic violence or abuse (more commonly cited among those first becoming homeless aged under 30 years) and financial difficulties and mental and other health issues (more commonly cited among those first becoming homeless over 30 years). These patterns are broadly in line with those reported for the smaller sample study of Smith et al. (2008). 4. Approach to estimation: a bivariate simultaneous durations model Our outcome variables are durations until transition from one state to another (the onset of homelessness and the onset of daily use of cannabis) and the causal effects of interest relate to the realization of one transition on the transition rate of the other. Given the structure of our model these are established by the timing of events conditional on observable and unobservable characteristics. According to Abbring and Heckman (2007) using bivariate duration models to identify treatment effects of this kind goes back to Freund (1961), where the model was applied to engine failures in twin-engine planes. Abbring and Heckman (2007) discussed the additional complications when attempting to model human behaviour in this way. Whereas the failure rates of machines may be constant over time, people may respond to the duration of the process in question. For example, an unemployed worker may lower his standards for accepting a job as the duration of unemployment increases. If so, the rate of transition from unemployment to a job may increase, and duration models need to account for this duration dependence. Furthermore, whereas machines may be very similar, unemployed individuals may not be, i.e. they may differ in (observed or unobserved) characteristics that may have differential effects on their rate of exit from unemployment. For example, more motivated unemployed workers are more likely to find a job quickly. The econometric framework of Abbring and Heckman (2007) accounts for this heterogeneity by including observable characteristics x as well as unobserved characteristics v, which are assumed to be temporally invariant, in a mixed proportional hazard model setup (see Van den Berg (2001)). Finally, whereas the failure of one machine is a random event, individuals may anticipate events. For example, an unemployed worker who knows exactly when a training programme starts may change his job search behaviour in anticipation of the start of the programme. Therefore, in this setting the identification of treatment effects relies on a no-anticipation assumption, which was set out formally, and discussed at length, in Abbring and van den Berg (2003) and again in Abbring and Heckman (2007). In this paper we specify a bivariate simultaneous duration model for the onset of homelessness and the onset of daily use of cannabis. In this model, each transition may causally affect the other transition rate, i.e. the realization of one duration can be considered as a treatment that causally affects the other duration through its transition rate. A major advantage of using this kind of approach is that, as shown by Abbring and van den Berg (2003), identification of the treatment effect does not rely on a standard conditional independence assumption we condi-

11 Drug Use and Onset of Homelessness 355 tion on both observables and jointly distributed unobservables and it is not necessary to have a valid instrument. Rather, identification comes from the timing of events, i.e. the order in which initiation into drug use and homelessness occurs. In this context the causal interpretation relies on the no-anticipation assumption and the estimation of unobserved heterogeneity. (Because of this advantage bivariate duration modelling has become an increasingly common approach in parts of the social policy literature, e.g. on the effect of benefit sanctions on welfare exit and job entry (see McVicar (2014) for a review). The bivariate duration approach has also been used in several studies of drug use effects, most commonly to investigate various effects of cannabis use (see Van Ours and Williams (2015) for a review). For applications to other questions see the references in Abbring and Heckman (2007).) Although Abbring and van den Berg (2003) demonstrated this for a bivariate duration model where one transition is (pre)defined as the treatment and the other the outcome, Abbring and Heckman (2007) showed that this naturally extends to the simultaneous case where each transition can impact the other. In all respects below we adopt the framework of Abbring and Heckman (2007). Let C.h/ be the duration until the onset of daily use of cannabis given the time of initiation into homelessness h, and let H(c) denote the duration until the onset of homelessness given the time of initiation into daily use of cannabis c. Assume that ex ante heterogeneity across agents is fully captured by observed characteristics x and unobserved characteristics v, which are assumed to be external and temporally invariant. Initiation into homelessness may causally affect the duration C.h/ through its transition (i.e. hazard) rate. Similarly, initiation into daily use of cannabis may causally affect the duration H.c/ through its hazard rate. Denote the hazard rate into daily use of cannabis at time t for an individual with characteristics.x, v c / as θ c.t x, h, v c /. Similarly the hazard rate into homelessness at time t for an individual with characteristics.x, v h / is θ h.t x, c, v h /. The unobservables v c and v h are from an unrestricted joint distribution.v c, v h / in which the unobservables may have elements in common. Both observables x and unobservables v c and v h capture ex ante heterogeneity, i.e. they are given at the start of the processes. The inclusion of correlated unobserved heterogeneity is an important feature of bivariate duration models that allows them to account for time invariant characteristics that, in our application, may lead individuals to be simultaneously more prone to substance use and to homelessness. (There might also be ex post shocks represented by exponential errors " c and " h. These shocks represent the randomness in the transition processes after conditioning on x, v and survival. Abbring and Heckman (2007) assumed that " c " h, so the potential outcomes are dependent only through the observed and unobserved characteristics.x, v/.) The no-anticipation condition excludes anticipation of future outcomes, i.e. there can be no anticipation of outcome C on the hazard of H and there can be no anticipation of outcome H on the hazard of C (Abbring and Heckman, 2007). Conditionally on observed characteristics and the distribution of unobserved heterogeneity, current hazards therefore depend only on past events and the transition processes evolve recursively. Formally, for all t R + : and θ c.t x, h, v c / = θ c.t x, h, v c / θ h.t x, c, v h / = θ h.t x, c, v h / for all h, h, c, c [t, /. Under this assumption Abbring and Heckman (2007) showed that such models are non-parametrically identified from single-spell duration data under the conditions for the identification of competing risks models based on multivariate mixed proportional hazards models.

12 356 D. McVicar, J. Moschion and J. C. van Ours The no-anticipation assumption implies that although individuals may have an expectation of an outcome occurring, because they cannot foresee the exact time that it will occur they do not change their (other outcome relevant) behaviour in anticipation of it. In our specific case, it requires that, conditionally on x and v, an individual does not alter her behaviour relevant to cannabis consumption because she knows that she will become homeless in a particular future year, and vice versa. We have already shown in Table 5 that the onset of homelessness is reportedly driven by a wide variety of factors, the most common of which involve actions by others (e.g. family members and carers, landlords and employers) which are not perfectly foreseeable by individuals and therefore not likely to change their behaviour in relation to cannabis use in advance. Similarly, the timing of initiation into regular drug use is likely to depend on imperfectly predictable factors such as the degree to which occasional drug use leads to addiction, which seem equally unlikely to change behaviour with respect to homelessness in advance. More generally, the violation of the no-anticipation assumption entails that individuals (a) have information regarding their future transition into the treatment (homelessness and daily use of cannabis), (b) know precisely when this transition will occur, (c) alter their behaviour with respect to the other outcome of interest in anticipation (daily use of cannabis and homelessness) and (d) that what led them to anticipate their transitions is not accounted for in the model (via observed or unobserved characteristics). It is in this sense that the no-anticipation assumption is arguably weaker than a standard conditional independance assumption (for a more detailed discussion see Lalive et al. (2008)). The hazard rate of initiation into daily use of cannabis at duration t conditional on observed and unobserved characteristics and whether or not an individual has been homeless before t is given by { λc.t/ exp.x θ c.t x, h, v c / = β c + v c / for t h, λ c.t/ exp.x.1/ β c + δ h + v c / for t>h. The hazard rate of initiation into homelessness at duration t conditional on observed and unobserved characteristics and whether or not an individual has started to use cannabis daily before t is given by { λh.t/ exp.x θ h.t x, h, v h / = β h + v h / for t c, λ h.t/ exp.x.2/ β h + δ c + v h / for t>c. The effect of previous use of cannabis on the onset of homelessness is measured by δ c. This is the key parameter of interest as it informs us about whether previous use of cannabis increases the risk of homelessness.δ c > 0/, reduces the risk of homelessness (δ c < 0) or has no direct effect on the likelihood of experiencing homelessness (δ c = 0). The other key parameter is the effect of previous onset of homelessness on initiation into daily use of cannabis, given by δ h. The baseline hazards λ c.t/ and λ h.t/ capture duration dependence of individual initiation rates. Furthermore, β h and β c are vectors of parameters capturing the effects of observable characteristics on the homelessness initiation rate and the initiation rate into cannabis use. In modelling the uptake of daily use of cannabis, we assume that potential exposure to drugs occurs from the age of 10 years. We model transitions up to and including age 30 years to capture early onset of drug use and early onset of homelessness. Individuals who have not started to use cannabis daily by age 25 years are very unlikely to do so later in their life (Van Ours, 2006a) and, as discussed in the previous section, onsets of homelessness in later life appear to be driven by a set of factors that is different from earlier onsets.

13 Drug Use and Onset of Homelessness 357 We model duration dependence in the cannabis initiation hazard in a flexible way by using a step function λ c = exp{σ k λ c,k I K.t/}, where k =.1, :::,10/ is a subscript for age categories and I k.t/ are time varying dummy variables that are 1 in the relevant category. We specify 10 age dummies, seven of which are for individual ages (age 12, :::, 18 years), whereas the first is for ages less than 12 years, the second last for ages between 19 and 21 years and the last interval is for ages from 22 years onwards up to 30 years. Because we also estimate a constant term, we normalize λ c,1 = 0. (As we know only the age at which each event first occurs and not the actual date, we cannot determine whether homelessness occurred first if both the onset of homelessness and substance use occurred at the same age. It is for this reason that we allow homelessness to impact on substance uptake if and only if it occurred in a previous period.) The conditional density function for the completed durations until the uptake of daily use of cannabis can be written as { t } f c.t x, h, v c / = θ c.t x, h, v c / exp θ c.s x, h, v c / ds :.3/ Individuals who have not used cannabis by the last age that they are observed in the survey are assumed to have a right-censored duration of non-use. In the initiation to the homelessness hazard, λ h.t/ represents individual duration dependence which is modelled by using a step function which is specified in the same way as for substance use. The conditional density function for the completed duration until first homelessness can be written as { f h.t x, c, v h / = θ h.t x, c, v h / exp 0 t 0 } θ h.σ x, c, v h / dσ :.4/ Individuals who have not experienced homelessness by the age at which they are last observed in the data are assumed to have a right-censored duration until the onset of homelessness. The potential correlation between the unobserved components in the hazard rates for substance uptake and homelessness is considered by specifying the joint density function for both durations of time until daily use of cannabis c and the duration of time until homelessness h conditional on x as f.c, h x/ = f c.t x, h, v c /f h.t x, c, v h / dg.v h, v c /:.5/ v h v c As is standard in recent applications of bivariate duration models, G.v h, v c / is assumed to be a flexible discrete distribution with an unknown number of points of support. We start by assuming that for every transition process its unobserved heterogeneity can be specified by a discrete distribution with two points of support. In combination this leads to four points of support:.v h1, v c1 /,.v h1, v c2 /,.v h2, v c1 / and.v h2, v c2 /, reflecting two types of individuals in the hazard rates for cannabis use (high susceptibility and low susceptibility) and two types in the hazard rate for homelessness (high susceptibility and low susceptibility). The four mass points imply that conditionally on observed characteristics there are four types of individuals. The associated probabilities are denoted as follows: Pr.v h = v h1, v c = v c1 / = p 1, Pr.v h = v h1, v c = v c2 / = p 2,.6/ Pr.v h = v h2, v c = v c1 / = p 3, Pr.v h = v h2, v c = v c2 / = p 4

14 358 D. McVicar, J. Moschion and J. C. van Ours with 0 p j 1forj = 1, :::, 4. These probabilities are modelled by using a multinomial logit specification, i.e. p j = exp.α j /={Σ j exp.α j /}, and we normalize α 4 = 0. Furthermore, because we also estimate constants we normalize v h1 = v c1 = 0. The parameter estimates are obtained by using the method of maximum likelihood considering that our duration information relates to intervals rather than to exact durations. For example, an individual who indicated that they became homeless at age 16 years may have become homeless on his 16th birthday or on the day before his 17th birthday. For this individual, we model that he did not yet start at age 15 years, but started before turning 17 years. A graphical explanation of this model is presented in Appendix A (Figs 4 and 5). The control variables that are included in our model are listed in Tables 1 and 2. They include three dummy variables for whether the respondent was not living with his parents at age 14 years because they were separated, because they were dead or because of conflict, three dummy variables for whether the respondent experienced emotional, physical or sexual abuse as a child and five dummy variables characterizing the behaviour of the main male and female caregivers of the respondent while growing up (substance abuse, incarceration, mental health problems, long-term unemployment and gambling issues). So, for example, if the male caregiver ever spent time in jail, this variable is coded 1, 0 if he did not spend time in jail, if the respondent had no male caregiver or if the information on the caregivers jail time was missing. Because some of this background information is missing for a significant portion of our sample (in some cases more than 10%), and because this is unlikely to be random, we also include dummy variables for missing information on control variables: one dummy for missingness on any of the reasons for not living with parents at age 14 years, one dummy for missingness on any of the childhood violence variables, one dummy for missingness on any of the male caregiver s information and one for the female caregiver s information. (Alternatives, including dropping observations for which there are missing data, are explored in a sensitivity analysis that is discussed in Section 5.2.) The missing dummies for the caregiver characteristics are coded 1 if the respondent had missing information on the presence of a caregiver or if any of the caregivers characteristics are missing, and 0 if none is missing. As a result, the caregivers variables capture the effect of having a caregiver with a certain negative characteristic (jail time, substance use, long-term unemployment, mental health issues and gambling issues) relative to caregivers with no known such issues or no caregiver. (Including specific dummy variables for respondents with no male or female caregiver to distinguish between those two reference categories does not alter the results. Indeed, the percentage of the reference category pertaining to no caregiver is relatively small (depending on the behaviour analysed, between 2.5% and 4.5% of the reference category did not have a female caregiver and between 14% and 19% did not have a male caregiver). And having no caregiver is very correlated with not living with one s parents at age 14 years, which we control for and appears to be the major divide in our sample: 46% of respondents were not living with their parents at age 14 years but, among those, only 3% could not identify a female caregiver and 19% could not identify a male caregiver.) 5. Results and discussion 5.1. Bivariate model for daily use of cannabis and first onset of homelessness Table 6 presents estimates of the bivariate model for initiation into daily use of cannabis and the onset of homelessness, allowing for causality in both directions. First we find evidence of the presence of unobserved heterogeneity. We can identify four mass points of which the distribution is given in Table 7. Thus conditionally on observed characteristics and age we can distinguish four types of individual with different predispositions to daily use of cannabis and homelessness.

15 Drug Use and Onset of Homelessness 359 Table 6. Bivariate simultaneous mixed proportional hazards model, daily use of cannabis and homelessness by age 30 years, coefficients (absolute t-statistics) Results for men Results for women Homelessness Cannabis daily Homelessness Cannabis daily Effect of cannabis daily on 0.53 (3.7) 0.13 (0.7) Effect of homelessness on 0.29 (1.7) 0.44 (2.2) Childhood Parents separated 0.60 (4.3) 0.32 (2.3) 0.68 (4.6) 1.03 (4.3) Parents dead 0.44 (1.8) 0.02 (0.1) 0.46 (1.6) 0.25 (0.6) Conflict parents 1.36 (6.1) 1.10 (4.0) 1.52 (7.7) 2.26 (6.9) Emotional abuse 0.59 (3.3) 0.10 (0.5) 0.79 (3.4) 0.38 (1.0) Physical violence 0.19 (1.0) 0.79 (3.9) 0.30 (1.3) 0.87 (2.2) Sexual violence 0.13 (0.7) 0.13 (0.7) 0.25 (1.7) 0.56 (2.1) Male caregiver Substance abuse 0.11 (0.7) 0.36 (2.4) 0.14 (0.8) 0.56 (2.2) Jail 0.01 (0.0) 0.37 (1.8) 0.24 (1.1) 0.18 (0.4) Hospital 0.49 (1.5) 0.09 (0.3) 0.02 (0.1) 0.07 (0.2) Unemployed 0.37 (2.1) 0.19 (1.0) 0.25 (1.2) 0.22 (0.8) Gambling 0.12 (0.5) 0.50 (2.2) 0.30 (1.3) 1.18 (3.1) Female caregiver Substance abuse 0.41 (2.1) 0.25 (1.3) 0.11 (0.5) 0.14 (0.5) Jail 0.34 (0.6) 0.56 (1.4) 0.72 (2.1) 1.89 (3.4) Hospital 0.70 (3.1) 0.23 (1.1) 0.72 (3.3) 0.93 (3.3) Unemployed 0.19 (1.5) 0.19 (1.3) 0.24 (1.6) 0.21 (0.9) Gambling 0.09 (0.4) 0.06 (0.2) 0.17 (0.7) 0.73 (2.0) Missing information Reason 0.61 (1.2) 0.01 (0.0) 1.47 (2.5) 0.04 (0.0) Violence 0.33 (1.5) 0.19 (0.9) 0.32 (1.5) 0.09 (0.2) Male caregiver 0.11 (0.5) 0.32 (1.5) 0.76 (3.4) 0.93 (2.5) Female caregiver 0.12 (0.6) 0.19 (0.8) 0.38 (1.8) 0.28 (0.6) Constant 6.57 (15.1) 5.40 (18.2) 7.57 (14.8) 6.47 (10.8) Age 12 years 0.20 (0.6) 0.65 (1.7) 0.87 (2.6) 1.03 (1.9) Age 13 years 0.25 (0.8) 1.61 (5.2) 1.30 (4.0) 2.03 (4.2) Age 14 years 1.04 (4.1) 2.01 (6.7) 2.08 (7.2) 2.88 (6.1) Age 15 years 1.61 (6.8) 2.31 (7.7) 2.87 (10) 3.09 (6.3) Age 16 years 2.08 (8.9) 2.84 (9.6) 3.18 (11) 3.96 (7.9) Age 17 years 2.35 (9.6) 2.78 (9.0) 3.38 (11) 3.70 (6.9) Age 18 years 2.22 (8.2) 2.68 (7.8) 3.48 (10) 3.95 (7.0) Age years 1.95 (7.0) 2.02 (5.9) 2.75 (7.6) 2.82 (4.5) Age 21 years 1.79 (5.7) 1.31 (3.4) 2.99 (7.8) 3.01 (4.8) v (7.3) 1.93 (7.3) 4.34 (11.4) α (1.6) 2.31 (3.1) α (0.7) 0.01 (0.1) α (3.1) 0.37 (1.3) Log-likelihood Absolute t-statistics are in parentheses; sample size, 639 women and 708 men. Significance at a 1% level. Significance at a 5% level. Significance at a 10% level.

16 360 D. McVicar, J. Moschion and J. C. van Ours Table 7. Distribution of unobserved heterogeneity Cannabis daily use by Cannabis daily use by men (%) women (%) High Low Total High Low Total Homeless low Homeless high Total Among men the largest group of 60% has a high predisposition to daily use of cannabis and homelessness whereas 11% has too low predispositions. This implies that for 71% of the men there is a positive correlation in unobserved characteristics affecting daily use of cannabis and homelessness. Failing to take this into account would lead to a spurious effect of cannabis use on homelessness or vice versa. The distribution of unobserved heterogeneity is different for women for whom the largest group of 41% combines a low predisposition to daily use of cannabis with a low predisposition to homelessness. However, since conditionally on observed characteristics and age 28% of the women combine positive predispositions to homelessness and daily cannabis, the majority of women (69%) also have a positive correlation in unobserved characteristics. Now consider impacts on the onset of homelessness for young men. Taking up daily use of cannabis is associated with a higher hazard rate for onset of homelessness than that of otherwise equivalent men who do not use cannabis daily by a factor of 1.7 and is statistically significant at the 1% level. (The proportional effect on the hazard rate the hazard ratio is given by exp.β/, i.e. exp.0:53/. Also note that measurement error in the age of onset of daily use of cannabis, whether stemming from systematic under-reporting or random recall error, may impart a downward bias on this estimate.) Under the assumptions that were set out in the previous section this can be plausibly interpreted as a causal effect. Possible causal mechanisms for such an effect include breakdown of family relationships and financial strain resulting from drug use (qualitative evidence for both was presented by Johnson and Chamberlain (2008)). These estimates provide the strongest quantitative evidence to date on the effect of use of cannabis on the onset of homelessness. They also add evidence of a further negative social outcome to the literature on the causal effects of cannabis use. The magnitude of this effect is similar to that of not living with one s parents because they are separated, having experienced emotional abuse as a child or having a female caregiver who had spent time in hospital because of mental health problems (all have similar signs and magnitudes and are statistically significant at 1%). The strongest association with the onset of homelessness among this sample comes from not living with one s parents at age 14 years because of conflict, which almost quadruples the hazard rate for the onset of homelessness. This is consistent with the high proportion of young men who cited this as a reason for first becoming homeless as presented in Table 5. Other factors with smaller magnitude but statistically significant effects are being orphaned by age 14 years, having a long-term unemployed male caregiver, and having a female caregiver with a substance abuse problem. These covariate parameter estimates reflect findings in the existing homelessness literature concerning the importance of adverse childhood experiences as predictors of homelessness (for example see van den Bree et al. (2009) and Shelton et al. (2009) and references therein).

17 Drug Use and Onset of Homelessness 361 We find little evidence of reverse effects from onset of homelessness to initiating daily use of cannabis for young men. The point estimate is actually negative, relatively small and only marginally statistically significant (at 10% but not 5%). (We show below that in most robustness tests it is negative, similar or smaller in magnitude, and statistically insignificant.) The strongest association with the take-up of daily use of cannabis is again conflict with parents (which triples the hazard rate), followed by experiencing physical violence as a child (which doubles the hazard rate). Other statistically significant factors include a male caregiver with substance abuse problems or who has spent time in prison. Data that enable a quantitative analysis of the effects of adverse childhood experiences such as these on cannabis use are rare, but existing studies have found a positive association between parental substance use and own drug use (e.g. DeSimone (2002) and Abelson et al. (2006)). The results for women are almost the polar opposite of those for men. We see no evidence of an effect of daily use of cannabis on onset of homelessness, but clear evidence of a reverse effect from homelessness to daily use of cannabis (the corresponding hazard ratio is 1.55). This gender contrast is to some extent visible in the raw data that were presented in Table 4, where the onset of homelessness more often precedes drug use uptake for women whereas the opposite is the case for men. Conflict with parents at age 14 years is again the variable with the strongest association with both outcomes. As for males, not living with one s parents at age 14 years because they are separated, emotional abuse, physical violence, male caregiver substance abuse and a female caregiver with prison time or hospital time for mental health problems are also associated with higher hazards for the onset of homelessness and/or take-up of daily use of cannabis. Note that reporting a male caregiver with a gambling problem again takes a negative sign. Experiencing sexual violence as a child is an additional factor that increases the hazard for both the onset of homelessness and daily use of cannabis for young women but not young men, as is missing data about the male caregiver. Ours is not the first study to find evidence of stronger effects of cannabis use for men than for women on social outcomes. Both DeSimone (2002) and Van Ours (2006b) found a weaker association for women than for men between cannabis or cocaine use and subsequent employment outcomes, which the latter speculated may reflect gender-specific unobservables such that women who were inclined to explore the drug scene in the past are more ambitious to find a job in the present. Other studies have also flagged potential gender differences specifically in the nature of the association between drug use and homelessness which are consistent with our results. For example, Smith et al. (2008) found that fewer women than men cite substance use as a reason for becoming homeless. This is consistent with the evidence from JH presented in Table 5. Instead women cite domestic violence much more frequently, both in the JH study and elsewhere (e.g. Lehmann et al. (2007)). Others have suggested that the tendency for women to have stronger social networks than men may act as a protective factor (Susser et al., 1993; Bassuk et al., 1997). Other potential protective factors that may play a bigger role for women than for men might include having caring responsibilties (and associated cash and other welfare benefits) for children (Bassuk et al., 1997). Possible causal mechanisms for the reverse effect from homelessness to cannabis use include adaptation to a subculture of substance use among the homeless and/or using substances as a coping mechanism (Johnson and Chamberlain, 2008). Kidd (2007) discussed whether young homeless women face greater adversity or perceive greater social stigma than young homeless men on average, which would be consistent with young homeless women disproportionately turning to drug use via one or both of the adaptation and coping mechanisms. Evidence that is suggestive of an effect of youth homelessness on drug use, both qualitative and quantitative, has